Method for detecting synchronicity between several digital measurement series with the aid of a computer

ABSTRACT

The method makes it possible to determine synchronicity of several measurement series which consist of binary frequency data, in order to detect redundancy between several neurons. In this case, every possible combination of synchronicity has its own occurrence probability. 
     The synchronicity is detected by measuring a discriminating significance, which tests a null hypothesis with a surrogate method. 
     One possible application is the detection of neuronal coding patterns in the brain.

BACKGROUND OF THE INVENTION

The invention relates to a method for detecting synchronicity betweenseveral digital measurement series with the aid of a computer.

When presented with measurement data given by time series, which forexample originate from different neurons, then it is of great interestto know with what probability synchronicity occurs between the variouspossible combinations of the binary signals of the time series.

FIG. 1 serves as an illustration. It shows three time series ZR1, ZR2and ZR3 by way of example. These time series may for example originatefrom different neurons or, in general, represent arbitrary binaryfrequency data. The order O is defined as being how many times seriesare taken into account for the synchronicity. In FIG. 1, the order O isequal to 3. For all possible combinations of the 3^(rd) order binarygroupings occurring in the example, a probability of synchronicityshould thus in each case be given. Thus, FIG. 1 indicates by way ofexample a combination Pat1 (011) which occurs two times.

The reference by T. M. Cover, "Elements of Information Theory, JohnWiley & Sons, 1976, pp. 18-23, ISBN 0-471-06259-6, discloses a methodfor determining a discriminating statistic.

SUMMARY OF THE INVENTION

The object of the invention is to provide a method for detectingsynchronicity between several digital measurement series, the methodbeing suitable in particular for detecting neuronal coding patterns inthe brain.

The method formulates a nonparametric statistical approach for detectingredundancy between several digital measurement series. A relevantconcrete example involves the synchronous firing of several neurons. Thesynchronicity is detected by measuring a discriminating significance,which tests a null hypothesis of independent firing with a surrogatemethod. The surrogate data used correspond to the null hypothesis of anoncausal relation between the firing or the nonfiring of several neurongroups. Rejection of the null hypothesis is based on the calculation ofthe discriminating statistic Λ of the original data record and of thediscriminating statistic D_(si) of the i-th surrogate data record whichhas been produced by making the null hypothesis.

As mentioned above, one refinement example of the method according tothe invention may be the firing of several neurons, the number of whichdetermines the order O, lying at the basis of the measurement series.The method according to the invention can therefore be used to solve thedifficult problem of detecting neuronal coding patterns in the brain.

BRIEF DESCRIPTION OF THE DRAWINGS

The features of the present invention which are believed to be novel,are set forth with particularity in the appended claims. The invention,together with further objects and advantages, may best be understood byreference to the following description taken in conjunction with theaccompanying drawings, in the several Figures of which like referencenumerals identify like elements, and in which:

FIG. 1 shows illustrative measurement data of various time series;

FIG. 2 shows a block diagram which represents the steps of the methodaccording to the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 indicates three different time series ZR1, ZR2 and ZR3 by way ofexample.

Generally, the order O is determined by the maximum number of "1s"occurring. In relation to an application example, the "1s" may beinterpreted as the firing of a neuron. There are generally 2^(O)different combinations in the case of O binary measurement series. Inthe example, the order is equal to three and there are eight differentbinary combinations. This example which is represented in FIG. 1 iscontinued in FIG. 2 in order to explain the method according to theinvention.

FIG. 2 represents a block diagram which contains the individual steps ofthe method according to the invention. With the aid of differentmeasurement series, which may originate from neurons, a real occurrenceprobability for each different binary combination is calculated (seestep 2a). This probability P is given as ##EQU1##

In relation to the example represented in FIG. 1, this means calculatingthe probability P for all possible binary combinations of thecorresponding order, that is to say for the triple

    {(000), (001), (010), (011), (100), (101), (110), (111)}   (3)

A discriminating statistic Λ is given by the T. M. Cover reference as(see FIG. 2, step 2b):

    Λ=R(x,z|y)-R(x,z),                         (4)

R(. . . ) denoting a redundancy,

x,y,z denoting an i-th order tuple consisting of the values of themeasurement series.

The formula (4) indicated here can be logically extended forhigher-order discriminating statistics.

The null hypothesis P* is determined in step 2c according to ##EQU2##

To explain formula (4) above, it may be mentioned that when there is anodd number of "1s" in the tuple, the sign is negative, otherwise it ispositive.

The pertubation variable w will be determined below such that thediscriminating statistic Λ gives a null result from the null hypothesis,i.e.

    Λ(P*)=0                                             (6),

With the condition that the pertubation variable w lies in a range

    W.sub.min <w<w.sub.max                                     (7a)

it being in this case necessary to respect the condition

    0<P* (1.sub.A)<1∀A                              (7b)

1_(A) denotes all possible permutations of "1s" in a tuple with power|A|. Additionally, a constraint is imposed according to the sum of alloccurrence probabilities of the null hypothesis: ##EQU3##

Using the null hypothesis P*, surrogate data records, i.e. arbitraryinstances of the null hypothesis condition, are determined by randomgenerator (step 2d). Expressed a different way, "dice are thrown" forthe measurement series, the "die" having the occurrence probabilityfixed by the null hypothesis for each possible combination.

The decision as to whether or not there is synchronicity, is determinedby a significance S (step 2e): ##EQU4##

An advantageous application of the method according to the inventionconsists, as mentioned above in the use of measurement series which arebased on the firing of real neurons. The method can equally be appliedto any binary frequency data.

The invention is not limited to the particular details of the methoddepicted and other modifications and applications are contemplated.Certain other changes may be made in the above described method withoutdeparting from the true spirit and scope of the invention hereininvolved. It is intended, therefore, that the subject matter in theabove depiction shall be interpreted as illustrative and not in alimiting sense.

What is claimed is:
 1. A method for detecting synchronicity betweenseveral digital measurement series using a computer, comprising thesteps of:a) using an order to indicate a number of measurement seriestaken into account which are to be examined for synchronicity; b)calculating an occurrence probability P_(j) for different binarycombination K_(j) such that ##EQU5## c) determining a discriminatingstatistic Λ depending on the order given in step a); d) forming a nullhypothesis, P*, such that ##EQU6## e) looking up a perturbation variablew such that

    Λ(P*)=0

W_(min) and W_(max) being defined such that

    0<P* (1.sub.A)<1∀A

with the constraint ##EQU7## f) determining surrogate data records,which are arbitrary instances of a condition of the null hypothesis P*:g) determining, for establishing existence of synchronicity, asignificance S such that ##EQU8##
 2. The method as claimed in claim 1,wherein time series of different neurons are used as the digitalmeasurement series.